Intel® oneAPI Math Kernel Library Developer Reference - C
Applies an elementary reflector as returned by p?tzrzf to a general matrix.
void pslarz (char *side , MKL_INT *m , MKL_INT *n , MKL_INT *l , float *v , MKL_INT *iv , MKL_INT *jv , MKL_INT *descv , MKL_INT *incv , float *tau , float *c , MKL_INT *ic , MKL_INT *jc , MKL_INT *descc , float *work );
void pdlarz (char *side , MKL_INT *m , MKL_INT *n , MKL_INT *l , double *v , MKL_INT *iv , MKL_INT *jv , MKL_INT *descv , MKL_INT *incv , double *tau , double *c , MKL_INT *ic , MKL_INT *jc , MKL_INT *descc , double *work );
void pclarz (char *side , MKL_INT *m , MKL_INT *n , MKL_INT *l , MKL_Complex8 *v , MKL_INT *iv , MKL_INT *jv , MKL_INT *descv , MKL_INT *incv , MKL_Complex8 *tau , MKL_Complex8 *c , MKL_INT *ic , MKL_INT *jc , MKL_INT *descc , MKL_Complex8 *work );
void pzlarz (char *side , MKL_INT *m , MKL_INT *n , MKL_INT *l , MKL_Complex16 *v , MKL_INT *iv , MKL_INT *jv , MKL_INT *descv , MKL_INT *incv , MKL_Complex16 *tau , MKL_Complex16 *c , MKL_INT *ic , MKL_INT *jc , MKL_INT *descc , MKL_Complex16 *work );
The p?larzfunction applies a real/complex elementary reflector Q (or QT) to a real/complex m-by-n distributed matrix sub(C) = C(ic:ic+m-1, jc:jc+n-1), from either the left or the right. Q is represented in the form
Q = I-tau*v*v',
where tau is a real/complex scalar and v is a real/complex vector.
If tau = 0, then Q is taken to be the unit matrix.
Q is a product of k elementary reflectors as returned by p?tzrzf.
(global)
if side = 'L': form Q*sub(C),
if side = 'R': form sub(C)*Q, Q = QT (for real flavors).
(global)
The number of rows in the distributed matrix sub(C). (m ≥ 0).
(global)
The number of columns in the distributed matrix sub(C). (n ≥ 0).
(global)
The columns of the distributed matrix sub(A) containing the meaningful part of the Householder reflectors. If side = 'L', m ≥ l ≥ 0,
if side = 'R', n ≥ l ≥ 0.
(local).
Pointer into the local memory to an array of size lld_v * LOCc(n_v) containing the local pieces of the global distributed matrix V representing the Householder transformation Q,
V(iv:iv+l-1, jv) if side = 'L' and incv = 1,
V(iv, jv:jv+l-1) if side = 'L' and incv = m_v,
V(iv:iv+l-1, jv) if side = 'R' and incv = 1,
V(iv, jv:jv+l-1) if side = 'R' and incv = m_v.
The vector v in the representation of Q. v is not used if tau = 0.
(global) The row and column indices in the global distributed matrix V indicating the first row and the first column of the matrix sub(V), respectively.
(global and local) array of size dlen_. The array descriptor for the distributed matrix V.
(global)
The global increment for the elements of V. Only two values of incv are supported in this version, namely 1 and m_v.
incv must not be zero.
(local)
Array of size LOCc(jv) if incv = 1, and LOCr(iv) otherwise. This array contains the Householder scalars related to the Householder vectors.
tau is tied to the distributed matrix V.
(local).
Pointer into the local memory to an array of size lld_c * LOCc(jc+n-1), containing the local pieces of sub(C).
(global)
The row and column indices in the global matrix C indicating the first row and the first column of the matrix sub(C), respectively.
(global and local) array of size dlen_. The array descriptor for the distributed matrix C.
(local).
Array of size lwork
If incv = 1,
if side = 'L' ,
if ivcol = iccol,
lwork ≥ NqC0
else
lwork ≥ MpC0 + max(1, NqC0)
end if
else if side = 'R' ,
lwork ≥ NqC0 + max(max(1, MpC0), numroc(numroc(n+icoffc,nb_v,0,0,npcol),nb_v,0,0,lcmq))
end if
else if incv = m_v,
if side = 'L' ,
lwork ≥ MpC0 + max(max(1, NqC0), numroc(numroc(m+iroffc,mb_v,0,0,nprow),mb_v,0,0,lcmp))
else if side = 'R' ,
if ivrow = icrow,
lwork ≥ MpC0
else
lwork ≥ NqC0 + max(1, MpC0)
end if
end if
end if.
Here lcm is the least common multiple of nprow and npcol and
lcm = ilcm( nprow, npcol ), lcmp = lcm / nprow,
lcmq = lcm / npcol,
iroffc = mod( ic-1, mb_c ), icoffc = mod( jc-1, nb_c ),
icrow = indxg2p( ic, mb_c, myrow, rsrc_c, nprow ),
iccol = indxg2p( jc, nb_c, mycol, csrc_c, npcol ),
mpc0 = numroc( m+iroffc, mb_c, myrow, icrow, nprow ),
nqc0 = numroc( n+icoffc, nb_c, mycol, iccol, npcol ),
ilcm, indxg2p, and numroc are ScaLAPACK tool functions; myrow, mycol, nprow, and npcol can be determined by calling the function blacs_gridinfo.
(local).
On exit, sub(C) is overwritten by the Q*sub(C) if side = 'L', or sub(C)*Q if side = 'R'.